Lecture 4
Thinking about the life
Zhanchun Tu ( 涂展春 )
Department of Physics, BNU
Email: [email protected]
Homepage: www.tuzc.org
Main contents
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The concepts of heat and free energy
●
How life generates order
●
How order is transmitted to the descendants
§4.1 Heat and free energy
Example 1: Freely falling ball
1
2
E =mgz m v
2
v
z
Vacuum box
m
Kinetic energy
Potential energy
Mechanical energy
v=−ż , v̇=g ⇒ Ė=0
Mechanical energy is conserved!
Example 2: Falling ball in mud
U =mgz
v
z
Box full of mud
m
decreases with time
1
2
T= mv
2
decreases with time finally
experience!
A mysterious “frictional” effect
in the mud drained off the
mechanical energy of the ball
●
Joule & Helmholtz
Friction converts mechanical into thermal energy.
When thermal energy is properly accounted for,
the energy accounts balance.
That is, the actual conserved
quantity is not the mechanical
energy, but the total energy,
the sum of the mechanical
energy plus heat.
What's friction? What's heat?
If energy is conserved, why
must we be careful not to
"waste" it?
What could "waste" mean?
●
What's friction?
–
not a process of energy loss
–
but rather of energy conversion
–
just as the falling ball converts potential to kinetic
energy
Energy can be partially
converted back to light
using a lamp
●
Energy conversion
–
we never get all the original energy back because
some is lost as heat
–
lost implies not that energy isn't conserved, but that
some of it makes a one-way conversion to heat
●
What could "waste" mean?
–
Even though energy is strictly conserved,
something has been wasted in example 2
–
To make a scientific theory of this something, we
need find a measurable quantity describing the
quality of energy
–
In this theory, we could assert that the sunlight, or
the potential energy has high quality while thermal
energy has poor quality
–
We also could try to argue that the quality of
energy always degrades in any transaction
History on heat
●
●
●
Franklin: fluid theory of heat
Thompson: find that heat production due to
friction ceases at the moment we stop doing
mechanical work on the system
Joule & Helmholtz: The heat produced by
friction is a constant × the mechanical work
done against that friction
(heat produced) = (mechanical energy input) × (0.24 cal/J)
[mechanical equivalent of heat]
First law of thermodynamics
●
●
Special form: Suppose a system undergoes a
process that leaves it in its original state (i.e.,
cyclic process). Then the net of the mechanical
work done on the system or by the system
equals the net of heat it gives off or takes in.
General form:
Energy is conserved
Note: R. Mayer (a doctor) first proposed the
concept of energy transaction and conservation
Question?
●
Ice refrigerator in a closed room
When the refrigerator
works, if we open its door,
does the temperature of
the room decreases?
What's heat
●
●
●
●
Mechanical equivalent of heat implies that heat is
a particular form of mechanical energy
Old idea (Newton): heat is the total kinetic energy
of the individual molecules constituting of a body
Heat is not fully equivalent to mechanical work
since one cannot be fully converted to the other
Thermal energy is a part of total energy
attributable to random molecular motion which is
distinct from the organized kinetic energy of a
falling ball
Quality of energy
●
●
We have known that heat has low quality. Thus
the random character must be the key to its
low quality.
We are proposing that
The distinction between high- and lowquality energy is a matter of organization
Concept of free energy
●
●
A quantity to measure the useful energy of a
system, the part of energy that can be
harnessed ( 利用 ) to do useful work
Idea: free energy F < energy E of the system,
by an amount related to the randomness, or
disorder of the system
●
Quantitative formula (See details in Lecture 5,6)
F=E-TS
S: entropy, describing the disorder
T: temperature
If the disorder is small enough, so that
TS E, then FE. We can say that the
system's energy is of high quality.
The principle of Minimum F
●
Example 1: falling ball in mud
1
2
E=mgz m v ET
2
Decreases
due to friction
ET: the thermal energy
of molecules in the ball
F=E-TS decreases
●
Example 2: free expansion of gas
(Assumption: constant T for environment)
More disorder,
S increases
F=E-TS decreases
●
Min F
A system at a fixed temperature T can
–
spontaneously drive a process if the
net effect of the process is to reduce
the system's free energy F
Free energy landscape
F
●
If the free energy is already at
a minimum, no spontaneous
change will occur.
Reaction coordinate
●
Self-assembly of a lipid bilayer
= N L / N
N = N L N W
a
LL
F 2 =V V
F 1=V
r
LW
N L vr
a
LW
−T S 2 A
−N L va
−TS 1
N [ ln 1−ln 1−]
v r , va  0
0
N L a0
v ≡v a v r − a 0
 F =−N v N T [ln 1−ln 1−]
f
F
v/T=1>0
self-assembly

F
v /T =−10
§4.2 How life generates order
The puzzle of biological order
●
Two examples
●
Second law of thermodynamics
In an isolated system molecular disorder
never decreases spontaneously !
●
Living things are full of exquisite structures.
Question: How they generate order?
●
Answer: The earth is not an isolated system.
Earth radiates
low quality heat
+ [life]
High quality
solar energy
Entropy changes due to the “Sun heats Earth, Earth heats outer space” process
Sun decreases in entropy while outer space increases in entropy.
Meanwhile, the Earth almost doesn't change its entropy,
but has the throughput ( 吞吐 ) shown.
The change in entropy of the biosphere each second due to
evolution of species is estimated as: -302 J/K << entropy throughput
[Styer, Am. J. Phys. 76 (2008) 1031]
●
Plants
●
Animals
Heat+O2
Light
H2O
CO2
●
Sugar
Structure
...
Sugar
Fat
O2
Heat
H2O+CO2
Tissue
Work
Life's trick
(1) Living things consume order, not energy
(2) The flow of energy through a system can leave behind increased order
●
Life doesn't really create order from nowhere.
●
Life captures order. This order then trickles
through ( 流经 ) the biosphere through a series
of transformation processes, which we will refer
to generically as free energy transductions.
●
Looking only at the biosphere, it seems as
though life has created order.
●
Homework: estimate the reasonable upper limit
Hint: surf on the internet
Paradigm for free energy transduction
●
Osmotic flow
H2O
sugar
VL+VR=const.
VL
VR
If load=0, small VR= high order; disorder
spontaneously increases = enlarge VR = pistons move
to the right. The end: VL vanishes.
We expect that if the load is small enough, it will be lifted!
But now VL is nonvanishing.
●
Questions
(1) Is the energy conserved in this process?
(2) Which energy is converted into mechanical energy?
Answers: (1) Yes. (2) Heat absorbed from the environment.
(3) Heat is low quality energy, why it can be converted
into the high quality mechanical energy?
Osmotic flow sacrifices molecular order,
to organize random thermal motion into
mechanical motion of a load.
●
Does the system's free energy reduce?
F =E−T S
=m g h−T f h/ L0 
0
R
L0 =V / A
f 
[The form of f in Lect. 5,6]
T f  h/ L0 
mgh
F reduces until a threshold hc!
−F
hc
h
●
What will happen when m increases?
mc gh
m2gh
Tf(h/L0)
m1 gh
m2>m1==>hc2<hc1
h c2
h c1
h
There exists mc, such that hc=0.
●
Guess the law of osmotic pressure
Osmotic pressure originates from the thermal motion of molecules
Dimensional analysis
 ∝n k B T r
compare
van't Hoff equation
 =n k B T r
●
Reverse osmosis (m>mc)
mgh
Tf  h / L 0
Pistons move to the left!
h
−F
The sugar is localized in the right side with
smaller volume, while the other side is full
of more pure water. The order increases!
●
Questions
(1) Is the energy conserved in this process?
(2) Where does mechanical energy go?
Answers: (1) Yes. (2) Giving off Heat.
●
Trick in the reverse-osmosis machine
Let energy pass through a system, it is
degraded from mechanical form to thermal
form while increasing its own order.
Free energy transducers
●
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Earth's biosphere
–
High quality solar energy→ low quality heat
–
Create order
Reverse-osmosis machine
–
High quality mechanical energy→ low quality heat
–
Create order
Molecular motors (in the latter lectures)
–
High quality chemical energy (ATP)→ low quality heat
–
Create order + movement
●
Two notes
–
Much of this course will be devoted to showing that
at a deep level these transducers, from the living to
nonliving worlds, are essentially the same.
–
the motors in living cells work better than simple
machines because evolution has designed them to
work better, not because of some fundamental
exception to physical law.
§4.3 How order is transmitted
to the descendants
A lesson from heredity ( 遗传 )
●
Aristotle
–
The male contributes the plan of
development and the female the
substrate ( 物质基础 )
–
The sperm contributes nothing to the
material body of the embryo ( 胚胎 ),
but only communicates ( 传达 ) its
program of development
Achievement: “plan of development”
Ignore: female also contributes the plan of development
●
Mendel (1865)
–
Experiment: 7 traits of Pisum sativum ( 豌豆 )
(1822-1884)
–
Discrete character of inheritance ( 遗传的颗粒性 )
●
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●
–
Simple biological traits are inherited in a discrete manner
Genetic code is a collection of switches (called “factors” )
Each factor could be set to two (or more) states
Mendel's law of inheritance
●
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Somatic cells ( 体细胞 ) carry two copies
of each factor, called diploid ( 二倍体 )
Germ cells ( 生殖细胞 ), formed by
meiosis ( 减数分裂 ), contain one copy of
each factor
Principle of independent assortment ( 独
立分配原则 ): meiosis chooses each
factor randomly and independently of the
others
Note: rediscovered by H. deVries, C. Correns, and E. von Tschermak until 1900
●
Sutton & Boveri's conjecture (1902-3)
–
●
Mendel's genetic factors were physical
objects---''genes'' located on the chromosomes
Morgan (1909-10)
–
Experiment: genetic linkage ( 遗传连锁 )
of Drosophila ( 果蝇 )
–
Conclusions:
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4mm
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The physical carriers of genetic information
are indeed the chromosomes
The chromosomes are chains of genes in a
fixed sequence
Both genes and their sequence are inherited
●
Müller and Timoféeff (1927)
–
Thermal motion becomes more destructive to the
order on smaller length scales.
–
How can genes be so tiny and yet so stable?
–
The most possible answer: chromosome is a single
molecule.
–
Experimental results
●
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Two kinds of radiation induce the
same mutations
The mutation rate depends linearly
on the radiation dose ( 剂量 )
●
Delbrück (1929): physical ideas
–
The density cion is a measurable
index of total radiation dose
–
Ions and other molecules form highly reactive
fragments. Some of them (the density c*=Kcion)
encounter and damage other nearby molecules
–
If gene is a single molecule, the breakage of a
chemical bond in it could induce a permanent change
in its structure, and so cause a heritable mutation
–
Suppose a fragment can wander
through a volume v before reacting
with something, and a gene has a
chance P1 of mutation if it is located
in this volume
Total probability of mutation = P1c*v = (P1Kv) × cion
Biological quantity
physical quantity
Agree with Timoféeff's experimental results!
–
Conclusions
●
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Gene is carried by a single long-chain molecule---polymer
Genetic information is long-lived because the chemical
bonds holding the molecule together require a high
activation energy to break.
●
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Schrödinger's summary (1944)
–
non-periodic string of monomers
–
If the gene is a molecule, which
of the many big molecules in
nucleus is it?
–
If mitosis involves duplication of
this molecule, then how does
such duplication work?
Watson & Crick (1953)
–
Double helix
Central dogma: flow of information
●
Original version
–
Crick (1958)
–
Temin (1963)
Valid for cells!
●
RNA viruses modify the central dogma
–
Influenza virus ( 流感病毒 ) has RNA as its genetic
material
transcription
translation
transcription
–
Human immunodeficiency virus (HIV) have RNA as
their genome, but do not replicate it as RNA-to-RNA
transcription
reverse transcription
translation
●
Genetic Code ( 遗传密码 )
–
Genetic information is encoded in mRNA in 3-letter units
20 amino acids, 1 start codon, 3 stop codons
§. Summary & further reading
Summary
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1st law: energy is conserved
2nd law: the isolated system will approach more
disorder
Min F: A system tends to reduce it's free energy
Life's trick: The flow of energy through a system
can leave behind increased order of the system
Central dogma:
Further reading
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Erwin Shrödinger, What is life? (1944) [Chinese
version http://www.oursci.org/lib/whatislife/index.htm]
方舟子 , 寻找生命的逻辑 ( 上海交通大学出版
社)
Philip Nelson, Biological Physics: Energy,
Information, Life (W. H. Freeman & Co., 2003)